Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

INTRODUCTION
the other of such as are fashioned from these. And the former
of things which have an essential subsistence; but the latter,of
such as exist only in conception. How, therefore, can the
mu1 which is a participant of intellect, and the first intellectual
essence, and which is from thence filled with knowledge and
life, be the receptacle of the most obscure forms, the lowest in
the order of things, and participating the most imperfect exq-
* In addition to the above excellent arguments from Proclus, I shall present the
IiberaI reader with what Syrianus the preceptor of Proclus says on the same subject,
in his commentary on the 13th book of Aristotle's Metaphysics, and which is as
follows: "We neither behold all the figures, nor all the numbers contained in sensiblcs,
nor is it possible for things derived from sensibles, to possess mathematical
accuracy and certainty. But if it should be said, that we add what is wanting,
and make the things abstracted from sensibles more certain, and after this manner
consider them; in the first place, indeed, it is requisite to say whence we derive
the power of thus giving them perfection. For we shall not find any cause more
true than that assigned by the ancients; I mean that the soul prior to the energies
of sense, essentially contains the reasons of all things. But in the next place, by
adding something to the things abstracted from sensibles, we do not make them
more certain and true, but, on the contrary more fictitious. For, if any one blames
the person of Socrates, while he accurately preserves in his imagination the image
which he has received from the sensible Socrates, he will have an accurate knowledge
of his person; but if he wishes to transform it into a more elegant figure,
he will rather consider the transformed figure than the form of Socrates. Nothing,
however, of this kind takes place in equal and similar numbers and figures; but
by how much the nearer we bring them to the more certain and perfect, they
become by so much the more manifest and known, in consequence of approaching
w much the nearer to their own impartible form. We may say indeed that we
are excited to the perception of mathematical truths by sensible objects; but it must
by no means be admitted that they derive their subsistence by an abstraction from
wnsibles. For the forms indeed, which are transmitted to us through the senses
may proceed as far as to the imagination, in which they wish to retain an individual
subsistence, and to continue such as they entered. When intellect, however,
afterwards passes beyond thew to universal, and to things which are apprehended
by scientific reasoning, it plainly evinces that it considers objects allied to itsclf,
and which indeed are its legitimate progeny. Hence, this energy is emulous of
divine energy, and not laborious, and has a power of exciting, purifying, and
enlightening the rational eye of the soul. But how could this be dfectcd, if it
mrc employed about things, which alone subsist by a denudation from sensibla?
In short, one of these two things must follow; either that mathematical demonstrations
are less certain than physiological arguments; or that the mathematical
sciences are conversant with things which possess more reality than the objects d
pbyks. For it is not reasonable to suppose that things which have mom of rality